Vortex instability of mixed convection boundary layer flow adjacent to a non-isothermal inclined surface in a porous medium with variable permeability

摘要

A linear stability theory is used to analyze the vortex instability of mixed convection boundary layer flow over an inclined heated surface in a porous medium with variable permeability. The variation of permeability in the vicinity of the solid boundary is approximated by an exponential function. The variation rate itself depends slowly on the streamwise coordinate, such as to allow the problem to possess a set of solutions, invariant under a group of transformations. The surface temperature is assumed to vary as a power function of the distance from the origin. In the main flow analysis, both the streamwise and normal component of the buoyancy force are retained in the momentum equations. The present formulation permits the angles of inclination ranging from 0 to close to 90 degrees from the horizontal. Local Nusselt number is presented for the uniform permeability (UP) and variable permeability (VP) cases. The critical Peclet numbers and the associated wave numbers are obtained for both the UP and VP cases. It is found that the VP effect tends to increase the heat transfer rate and destabilize the flow to the vortex mode of disturbance. (C) 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.